Market prices for various items

All regular items (weapons/armor) are sold at the same fraction of their worth, which is the selling price modifier for that settlement. Price modifiers are expressed as a percentage of its worth: ie a Full Helm is worth 3500, if it sells for 689G in a settlement, we know the selling price modifier in that settlement is more than 19.686% (689/3500) and less than 19.714% (690/3500) as prices are truncated. Selling price modifiers are a good deal higher for treasure items (prices about equal to worth are common) and trade goods (prices often higher than worth).

Similarly, there is a buying price modifier for each settlement, which determines buying prices for all regular items for that settlement. Example, a Marketplace in a Castle settlement selling a Militia Spear (worth 180) for 200 would have a buying price modifier of 1.11. Trade goods purchase also use the same buying price modifier. Supplies (tools/medicine/ammo) purchase generally also use the same buying price modifier, but in some settlements, buying prices can be 1.5x of what is expected. If a settlement has an attached location that produces the item in question (ie Arrow-Maker Shed produces Ammo, Wheat Fields produce Ground Grains), it will be unusually low in price.

Buying price modifiers are correlated with selling price modifiers for any given settlement. Essentially, settlements with high buying price modifiers will also have high selling price modifiers, ditto for low price modifiers.
Example: On Veteran economic difficulty, a Stronghold where Tools can be bought for 244G (buying price modifier = 244/200 = 1.22), also gives 329G for selling a Warbrand (selling price modifier = 329/1800 = 0.1828). Another settlement, a Village may have cheaper Tools at 208G (buying modifier 1.04), but only gives 280G for Warbrands (selling modifier 0.1556). Buying price modifier/Selling price modifier = 6.67 (approx) in both cases. And this ratio applies to all settlements when playing on Veteran difficulty (all other factors being equal: Neutral (50) Relations, no settlement status modifiers).
Expert Economic difficulty has a higher ratio (approx 7.41) due to lower Selling price modifiers.

Assuming Expert economic difficulty, for settlements at Neutral relations, with no settlement status modifiers, selling price modifier for regular items (weapons/armor/pelts/fangs) usually ranges from 12.82% to 17.69% over various settlements.

For example, increasing Relations from 50 to 100 will improve selling price modifiers for regular items in a City Hall from 17.69% to 19.69%. The same increase in Relations improves selling price modifiers for treasure items from 112.0% to 124.8% (112.0/17.69 = 124.8/19.69 = 6.33)

1)Economic difficulty - this is set by the player before the start of any campaign and affects selling prices, with Expert naturally having lower selling prices compared to Beginner/Veteran. For example, on Veteran, base selling price modifiers for City Halls are 18.73% - 19.61%. On Expert the corresponding range is 16.88% - 17.69%.

2)Settlement type/size - this determines the base price modifiers for each settlement and are quite variable.
They can be grossly grouped into 3 'price modifier brackets' (High, Medium, Low).
Assuming Expert economic difficulty, no Relation modifiers (Relation 50) and no Settlement status modifiers:

Type

Sellmodif

Buymodif

High

City Hall, Stronghold

0.1769, 0.1727, 0.1688, 0.1647

1.31, 1.28, 1.25, 1.22

Medium

Town Hall, Castle

0.1539, 0.1498, 0.1457

1.14, 1.11, 1.08

Low

Village Hall, Fortified Manor

0.1404, 0.1364, 0.1323, 0.1282

1.04, 1.01, 0.98, 0.95

The table above shows that City Halls generally give the best base selling prices while Village Halls and Fortified Manors generally have the cheapest buying prices.
There are sometimes a few discrepancies over time. This may be due to locations being rebuilt (from ruins) or getting destroyed in raids. But generally base price modifiers for a given settlement stay constant over the course of a campaign, all other factors below being equal.

3)Settlement relations - doing contracts for a settlement improves Relations (starts at Neutral(50) and is capped at Allied (100)).
On Expert difficulty, the maximum increase is about "2% of worth" for selling price modifiers and this appears to be factored in additively as opposed to settlement status modifiers.
For example, a City Hall may start at 17.69% selling price modifier at 50 Relations. This improves to 19.69% at 100 Relations. A Village Hall would start lower at 13.64% selling price modifier at 50 Relations. This improves to 15.64% at 100 Relations.

On Expert difficulty, the maximum decrease is about "15% of worth" for buying price modifiers.
For example, a Village Hall may start at 1.04 buying price modifier at 50 Relations, which goes down to 0.89 buying price modifier at 100 Relations. This is factored in additively as well.

The rate of Relations decay is slow for regular settlements. A completed contract typically gives roughly +8 Relations and it takes about 33 days before Relations resets back to 50 (disappears from list of settlements on Factions screen).

4)Settlement status - discussed in more detail here
These are applied multiplicatively on price modifiers after Relations has been factored in. For example, a City Hall at 100 Relations may start with 19.69% as its selling price modifier. Ambushed Trade Routes applies a further 10% and increases selling price modifier to 21.66% (19.69*1.1).
In brief, favorable statuses for selling items: Ambushed Trade Routes (10%), Safe Roads (9%), High Spirits (5%)
And favorable statuses for buying items: Well Supplied (-10%), High Spirits (-5%)